Description
A method to calculate instanton corrections to the non-perturbative effects of the topological string is by finding the Gromov-Witten (GW) invariants. They are rational numbers that appear in the enumerative geometry of Calabi-Yau 3-folds and have applications in string theory. They arise in the topological A-model as counts of worldsheet instantons. GW invariants are also present in quantum K-theory; however, in this context these numbers are integers. The invariants in K-theory have an interpretation of BPS objects in 3 dimensions (on the 3d world volume). In this work, we use the Atiyah-Bott localization method to compute the GW invariants in both contexts: quantum cohomology and quantum K-theory, for local Calabi-Yau manifolds. The final goal is to compare the results in both theories and provide an interpretation within string theory.
